Results from direct detection experiments are typically interpreted by employing an assumption about the dark matter velocity distribution, with results presented in the mχ – σn plane. Recently methods which are independent of the DM halo velocity distribution have been developed which present results in the vmin – g~ plane, but these in turn require an assumption on the dark matter mass. Here we present an extension of these halo-independent methods for dark matter direct detection which does not require a fiducial choice of the dark matter mass. With a change of variables from vmin to nuclear recoil momentum (pR), the full halo-independent content of an experimental result for any dark matter mass can be condensed into a single plot as a function of a new halo integral variable, which we call tilde h(pR). The entire family of conventional halo-independent tilde g~(vmin) plots for all DM masses are directly found from the single tilde h~(pR) plot through a simple rescaling of axes. By considering results in tildeh~(pR) space, one can determine if two experiments are inconsistent for all masses and all physically possible halos, or for what range of dark matter masses the results are inconsistent for all halos, withoutmore » the necessity of multiple tilde g~(vmin) plots for different DM masses. As a result, we conduct a sample analysis comparing the CDMS II Si events to the null results from LUX, XENON10, and SuperCDMS using our method and discuss how the results can be strengthened by imposing the physically reasonable requirement of a finite halo escape velocity.« less